An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. It was also the era of new math. Introduced to US schools in the late 1950s and 1960s, the new math was a curricular answer to Cold War fears of American intellectual inadequacy. In the age of Sputnik and increasingly sophisticated technological systems and machines, math class came to be viewed as a crucial component of the education of intelligent, virtuous citizens who would be able to compete on a global scale. In this history, Christopher J. Phillips examines the rise and fall of the new math as a marker of the period's political and social ferment. Neither the new math curriculum designers nor its diverse legions of supporters concentrated on whether the new math would improve students' calculation ability. Rather, they felt the new math would train children to think in the right way, instilling in students a set of mental habits that might better prepare them to be citizens of modern society a world of complex challenges, rapid technological change, and unforeseeable futures. While Phillips grounds his argument in shifting perceptions of intellectual discipline and the underlying nature of mathematical knowledge, he also touches on long-standing debates over the place and relevance of mathematics in liberal education. And in so doing, he explores the essence of what it means to be an intelligent American by the numbers.

Vito Volterra (1860-1940) was one of the most famous representatives of Italian science in his day. Angelo Guerragio and Giovanni Paolini analyze Volterra s most important contributions to mathematics and their applications, as well as his outstanding organizational achievements in scientific policy. Volterra was one of the founding fathers of functional analysis and the author of fundamental contributions in the field of integral equations, elasticity theory and population dynamics (Lotka-Volterra model). He delivered keynote lectures on the occasion of the International Congresses of Mathematicians held in Paris (1900), Rome (1908), Strasbourg (1920) and Bologna (1928). He became involved in the scientific development in united Italy and was appointed senator of the kingdom in 1905. One of his numerous non-mathematical activities was founding the National Research Council (Consiglio Nazionale delle Ricerche, CNR).During the First World War he was active in military research. After the war he took a clear stand against fascism, which was the starting point for his exclusion. In 1926 he resigned as president of the world famous Accademia Nazionale dei Lincei and was later on excluded from the academy. In 1931 he was one of the few university lecturers who denied to swear an oath of allegiance to the fascistic regime. In 1938 he suffered from the impact of the racial laws. The authors draw a comprehensive picture of Vito Volterra, both as a great mathematician and an organizer of science.

How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.

This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Greeks, followed by the period beginning in the 16th century. For several centuries the main scientific challenge concerned the mechanics of planetary dynamics, and the book describes the basic numerical methods of that time. In turn, at the end of the Second World War scientific computing took a giant step forward with the advent of electronic computers, which greatly accelerated the development of numerical methods. As a result, scientific computing became established as a third scientific method in addition to the two traditional branches: theory and experimentation. The book traces numerical methods' journey back to their origins and to the people who invented them, while also briefly examining the development of electronic computers over the years. Featuring 163 references and more than 100 figures, many of them portraits or photos of key historical figures, the book provides a unique historical perspective on the general field of scientific computing - making it a valuable resource for all students and professionals interested in the history of numerical analysis and computing, and for a broader readership alike.

Winner of the 1983National Book Award

..".a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983National Book Award edition)

Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications.

The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.

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Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses. Classroom-tested at Notre Dame University, this textbook is suitable for students of wide-ranging backgrounds because it engages its subject at several levels and offers ample and flexible problem set options for instructors. Parts I and II are both supplemented by expansive Problems and Projects segments. Topics covered in the book include: * the basics of geometry, trigonometry, algebra, and coordinate geometry and the historical, scientific agenda that drove their development* a brief, introductory calculus from the works of Newton and Leibniz* a modern development of the essentials of differential and integral calculus* the analysis of specific, relatable applications, such as the arc of the George Washington Bridge; the dome of the Pantheon; the optics of a telescope; the dynamics of a bullet; the geometry of the pseudosphere; the motion of a planet in orbit; and the momentum of an object in free fall. Calculus in Context is a compelling exploration-for students and instructors alike-of a discipline that is both rich in conceptual beauty and broad in its applied relevance.

Code 19 provides a powerful evidence for God's existence, as expected, envisioned or demanded by some philosophers and scientists, such as Galileo Galilei, Isaac Newton, Gottfried Leibniz, David Hume, Paul Dirac, and Carl Sagan.Code 19 was hidden in the 74th chapter of the Quran The Hidden, for 19x74 (1406) lunar years, and was discovered in 1974 by my colleague, Dr. Rashad Khalifa, an Egyptian-American biochemist. The number 19 has been a major controversy since its discovery and the number has realized all its assigned functions according to the prophetic verses of Chapter 74.Because of the implications of his discovery of the Secret, as well as his strong criticism of the sectarian teachings based on Hadith and Sunna, Rashad was declared a heretic/apostate by leading Sunni scholars from 38 countries who held an emergency conference in Saudi Arabia in 1989 to discuss the Salman Rushdie controversy. While Rushdi survived, Rashad was assassinated in this Masjid in January 31, 1990, by a terrorist group linked to al-Qaeda. The author of this book also received similar fatwa, yet he has escaped several assassination attempts, so far.Code 19, which was also discovered in the original portions of the Old Testament by Judah ben Samuel in 11th century, is simple to understand but impossible to imitate.Code 19 has little to do with numerology, since its literary-numerical (LitNu) pattern can be verified or falsified through scientific inquiry. It is radically different from the pattern demonstrated in The Bible Code, which has no statistical value.Unlike regular metaphysical or paranormal claims, Code 19 can be verified or falsified by virtually anyone, since the Arabic version of the Quran is available everywhere. Besides, for the most part, the reader does not need to know Arabic but only two eyes to see, an ability to count, a critical mind, and an open mind and heart to witness extraordinary signs as the fulfillment of a great prophecy.This discovery has created a paradigm change among those who witness it: instead of joining a religious bandwagon by blindly believing a holy story or hearsay, we must be critical thinkers; we must question everything and seek truth through knowledge. The code suggests a "Copernican revolution" in theology of religions. Instead of Krishna-centered, or Jesus-centered, or Muhammad-centered religions we must turn to the original center, to the God-centered model. The message of rational monotheism has sparked an ongoing controversy in countries with Muslim-majority populations, e.g., Egypt, Pakistan, Malaysia, Saudi Arabia, Turkey, etc. Internet forums are filled with heated debates regarding this code.The improbability and impossibility of the numerical structure of the Quran being produced by a medieval Arab genius becomes evident when we consider the following factors: It includes simple elements of the Quran and goes deeper to an interlocking system of complex numerical patterns and relationships. It involves not only frequencies of letters and words but also the numerical values of letters. It involves not only an intricate numerical pattern but also a huge set of data consisting of units with multiple functions, such as letters that are also digits, words that are also numbers. The nemeroliteral aspect of the Quran were not known by the adherents of the Quran until late 1960s and especially, 1974. The literary aspect of the Quran has received praises from many literary giants throughout centuries. The scientific accuracy of Quranic statements on various fields has been immaculate. Muhammad was one of the busiest and greatest social and political reformists in human history. The timing of the discovery of the code is precise and prophetic. A series of prophetic events regarding the code has been fulfilled.

This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d'Alembert and Euler; Fourier's solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincare on the hypergeometric equation; Green's functions, the Dirichlet principle, and Schwarz's solution of the Dirichlet problem; minimal surfaces; the telegraphists' equation and Thomson's successful design of the trans-Atlantic cable; Riemann's paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard. The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.

The novel use of symbolism in early modern mathematics poses both philosophical and historical questions. How can we trace its development and transmission through manuscript sources? Is it intrinsically related to the emergence of symbolic algebra? How does symbolism relate to the use of diagrams? What are the consequences of symbolic reasoning on our understanding of nature? Can a symbolic language enable new forms of reasoning? Does a universal symbolic language exists which enables us to express all knowledge?This book brings together a collection of papers that address all these and related questions ? which were initially posed on a conference held in Ghent (Belgium) in August 2009. Scholars working on philosophy of science, history of philosophy and history of mathematics provide an insight into the role and function of symbolic representations in the development of early modern mathematics. The papers cover the period from early abbaco arithmetic and algebra (14th century) up to Leibniz (early 18th century).

Science, with its inherent tension between the known and the unknown, is an inexhaustible mine of great stories. Collected here are twenty-six among the most enchanting tales, one for each letter of the alphabet: the main characters are scientists of the highest caliber most of whom, however, are unknown to the general public. This book goes from A to Z. The letter A stands for Abel, the great Norwegian mathematician, here involved in an elliptic thriller about a fundamental theorem of mathematics, while the letter Z refers to Absolute Zero, the ultimate and lowest temperature limit, - 273,15 degrees Celsius, a value that is tremendously cooler than the most remote corner of the Universe: the race to reach this final outpost of coldness is not yet complete, but, similarly to the history books of polar explorations at the beginning of the 20th century, its pages record successes, failures, fierce rivalries and tragic desperations. In between the A and the Z, the other letters of the alphabet are similar to the various stages of a very fascinating journey along the paths of science, a journey in the company of a very unique set of characters as eccentric and peculiar as those in Ulysses by James Joyce: the French astronomer who lost everything, even his mind, to chase the transits of Venus; the caustic Austrian scientist who, perfectly at ease with both the laws of psychoanalysis and quantum mechanics, revealed the hidden secrets of dreams and the periodic table of chemical elements; the young Indian astrophysicist who was the first to understand how a star dies, suffering the ferocious opposition of his mentor for this discovery. Or the Hungarian physicist who struggled with his melancholy in the shadows of the desert of Los Alamos; or the French scholar who was forced to hide her femininity behind a false identity so as to publish fundamental theorems on prime numbers. And so on and so forth. Twenty-six stories, which reveal the most authentic atmosphere of science and the lives of some of its main players: each story can be read in quite a short period of time -- basically the time it takes to get on and off the train between two metro stations. Largely independent from one another, these twenty-six stories make the book a harmonious polyphony of several voices: the reader can invent his/her own very personal order for the chapters simply by ordering the sequence of letters differently. For an elementary law of Mathematics, this can give rise to an astronomically large number of possible books -- all the same, but - then again - all different. This book is therefore the ideal companion for an infinite number of real or metaphoric journeys.

Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: * Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics * Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. * Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Every day we produce loads of data about ourselves simply by living in the modern world: we click web pages, shop with credit cards, and make cell phone calls. Companies like Yahoo! and Google are harvesting an average of 2,500 details about each of us every month. Who is looking at this data and what are they doing with it? Journalist Stephen Baker explores these questions and provides us with a fascinating guide to the world we're entering--and to the people controlling that world. The Numerati have infiltrated every realm of human affairs, profiling us as workers, shoppers, voters, potential terrorists--and lovers. The implications are vast. Privacy evaporates. Our bosses can monitor our every move. Retailers can better tempt us to make impulse buys. But the Numerati can also work on our behalf, diagnosing an illness before we're aware of the symptoms, or even helping us find our soul mate. Entertaining and enlightening, "The Numerati" shows how a powerful new endeavor--the mathematical modeling of humanity--will transform every aspect of our lives.

"O'Shea tells the fascinating story of this mathematical mystery and its solution by the eccentric Mr. Perelman."--"Wall Street Journal

"In 1904, Henri Poincare, a giant among mathematicians who transformed the fledging area of topology into a powerful field essential to all mathematics and physics, posed the Poincare conjecture, a tantalizing puzzle that speaks to the possible shape of the universe. For more than a century, the conjecture resisted attempts to prove or disprove it. As Donal O'Shea reveals in his elegant narrative, Poincare's conjecture opens a door to the history of geometry, from the Pythagoreans of ancient Greece to the celebrated geniuses of the nineteenth-century German academy and, ultimately, to a fascinating array of personalities--Poincare and Bernhard Riemann, William Thurston and Richard Hamilton, and the eccentric genius who appears to have solved it, Grigory Perelman. The solution seems certain to open up new corners of the mathematical universe.

A New York Times Bestseller Arthur Benjamin . . . joyfully shows you how to make nature's numbers dance." ,Bill Nye The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples,from ice-cream scoops and poker hands to measuring mountains and making magic squares,this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike. A positively joyful exploration of mathematics." , Publishers Weekly , starred review Each [trick] is more dazzling than the last." , Physics World

This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.

A Nobel Prize-winning physicist argues that beauty is the fundamental organizing principle for the entire universe In this scientific tour de force, world-class physicist Frank Wilczek argues that beauty is at the heart of the logic of the universe. As the quest to find the beauty embodied in the universe has connected all scientific pursuit, from Pythagoras to Einstein, Wilczek shows us just how deeply intertwined our ideas about beauty and art are with our understanding of the cosmos. A Beautiful Question is a mind-expanding book combining the age-old human quest for beauty with the age-old human quest for truth.

An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. It was also the era of new math. Introduced to US schools in the late 1950s and 1960s, the new math was a curricular answer to Cold War fears of American intellectual inadequacy. In the age of Sputnik and increasingly sophisticated technological systems and machines, math class came to be viewed as a crucial component of the education of intelligent, virtuous citizens who would be able to compete on a global scale.
In this history, Christopher J. Phillips examines the rise and fall of the new math as a marker of the period's political and social ferment. Neither the new math curriculum designers nor its diverse legions of supporters concentrated on whether the new math would improve students' calculation ability. Rather, they felt the new math would train children to think in the right way, instilling in students a set of mental habits that might better prepare them to be citizens of modern society--a world of complex challenges, rapid technological change, and unforeseeable futures. While Phillips grounds his argument in shifting perceptions of intellectual discipline and the underlying nature of mathematical knowledge, he also touches on long-standing debates over the place and relevance of mathematics in liberal education. And in so doing, he explores the essence of what it means to be an intelligent American--by the numbers.

Der Band enthalt 14 Korrespondenzen Eulers mit Gelehrten aus dem Umfeld der Universitat Halle, der damals groessten und bedeutendsten Universitat in Preussen. Er umfasst mehr als zweihundert Briefe aus der Zeit, als Euler in Berlin Direktor der Mathematischen Klasse der preussischen Akademie der Wissenschaften war und engen Kontakt zur Petersburger Akademie der Wissenschaften pflegte. Abgesehen von drei lateinischen Briefen, die von den Herausgebern ubersetzt wurden, sind alle Briefe in deutscher Sprache abgefasst. Die Briefpartner waren in der Zeit ihrer Korrespondenz mit Euler zwischen 20 und 60 Jahre alt. Viele der jungeren beschreiben ihre berufliche Situation und bitten Euler um Empfehlungen und Protektion, wahrend altere auch technische und mathematische Probleme eroertern und sich dabei als durchaus ebenburtige Partner erweisen. Dazu kommen Verhandlungen im Zusammenhang mit der Besetzung von Professorenstellen, die Euler im Auftrag Friedrichs II. fuhrte. Neben dem unmittelbaren und anschaulichen Einblick in das akademische Leben des 18. Jahrhunderts und speziell in die Zustande an der halleschen Universitat bezeugen viele Briefe die Sorgen und Belastungen, welche die Zeitumstande, insbesondere der Siebenjahrige Krieg, fur die Bewohner der Stadt Halle mit sich brachten. This volume of the Opera omnia contains Euler's correspondence with scientists connected to the University of Halle, the most prestigious Prussian university in the 18th century. It includes more than 200 letters dating from the period when Euler served as director of the class of mathematics of the Prussian Academy of Sciences in Berlin, yet still remained in close contact with the Russian Academy of Sciences in St. Petersburg. Except for three letters written in Latin and translated into German by the editors, all the letters were originally written in German. At the time when the correspondents were in touch with Euler, their ages varied between twenty and sixty years old. Many of the younger ones were dissatisfied with their professional situation and asked Euler for support or for letters of recommendation, whereas some of the older correspondents discussed high-level technical and mathematical problems as equal partners of the Berlin mathematician. Additional letters reveal negotiations with scientists who were being considered for university professorships by the Prussian King Frederick II. The letters provide an immediate and vivid insight into academic life, and in particular, into working conditions, at the University of Halle at the time of Euler. They shed light on the worries and hardships endured by the population of that city during the Seven Years' War and other contemporary events.

An easy-to-read presentation of the early history of mathematics Engaging and accessible, An Introduction to the Early Development of Mathematics provides a captivating introduction to the history of ancient mathematics in early civilizations for a nontechnical audience. Written with practical applications in a variety of areas, the book utilizes the historical context of mathematics as a pedagogical tool to assist readers working through mathematical and historical topics. The book is divided into sections on significant early civilizations including Egypt, Babylonia, China, Greece, India, and the Islamic world. Beginning each chapter with a general historical overview of the civilized area, the author highlights the civilization s mathematical techniques, number representations, accomplishments, challenges, and contributions to the mathematical world. Thoroughly class-tested, An Introduction to the Early Development of Mathematics features: * Challenging exercises that lead readers to a deeper understanding of mathematics * Numerous relevant examples and problem sets with detailed explanations of the processes and solutions at the end of each chapter * Additional references on specific topics and keywords from history, archeology, religion, culture, and mathematics * Examples of practical applications with step-by-step explanations of the mathematical concepts and equations through the lens of early mathematical problems * A companion website that includes additional exercises An Introduction to the Early Development of Mathematics is an ideal textbook for undergraduate courses on the history of mathematics and a supplement for elementary and secondary education majors. The book is also an appropriate reference for professional and trade audiences interested in the history of mathematics. Michael K. J. Goodman is Adjunct Mathematics Instructor at Westchester Community College, where he teaches courses in the history of mathematics, contemporary mathematics, and algebra. He is also the owner and operator of The Learning Miracle, LLC, which provides academic tutoring and test preparation for both college and high school students.

This volume of the Opera omnia includes Euler's correspondences in French with his Swiss countrymen Louis Bertrand, Charles Bonnet, Marc-Michel Bousquet, Jean de Castillon, Gabriel Cramer, Philibert Cramer, Gaspard Cuentz, Albrecht von Haller, Georges-Louis Lesage et Johann Caspar Wettstein, and one letter to the German Johann Michael von Loen who is mentioned in the Euler-Bertrand correspondence. The first letter from Euler to d'Alembert recently rediscovered has been added as supplement. Whereas the correspondence with Gabriel Cramer and Georges-Louis Lesage deals mainly with mathematical and physical subjects (Cramer's rule, Cramer's paradox, Lesage's theory of gravity), many letters exchanged with other Swiss correspondents provide new information about Euler's non-scientific activities, like the commerce of almanacs, negotiations with publishers, the support of young scientists in search of a position, and a variety of private matters. ----- Ce volume contient les correspondances qu'Euler a entretenues avec plusieurs compatriotes suisses en langue francaise. Il s'agit de Louis Bertrand, Charles Bonnet, Marc-Michel Bousquet, Jean de Castillon, Gabriel Cramer, Philibert Cramer, Gaspard Cuentz, Albrecht von Haller, Georges-Louis Lesage et Johann Caspar Wettstein. Bien qu'il n'ait pas ete suisse, une lettre de Johann Michael von Loen, personnage mentionne dans la correspondance Euler-Bertrand, figure egalement dans ce volume. De plus, la premiere lettre d'Euler a d'Alembert recemment redecouverte a ete ajoutee en annexe. Tandis que les correspondances avec Gabriel Cramer et Georges-Louis Lesage portent essentiellement sur des sujets de mathematiques et de physique (regle de Cramer, paradoxe de Cramer, theorie de la gravitation de Lesage), une grande partie des lettres qu'Euler a echangees avec d'autres compatriotes refletent ses activites non scientifiques, comme le commerce d'almanachs, les negociations avec des editeurs-imprimeurs a propos de la publication de ses ouvrages, ses interventions en faveur de jeunes scientifiques a la recherche d'un poste, et des affaires privees.

Paul Benacerraf has dominated the philosophy of mathematics in the past 25 years. Arguments derived from Benacerraf's analyses of the concept of number and the tension between the epistemology and the semantics of matematics are widespread in the rest of philosophy, particulary the philosophy of langauge and metaphysics.

This volume contains ten original essays discussing Benacerrafian themes within and outside the philosophy of mathematics, and a new essay, "What mathematical truth could not be" by Benaceraff. Within the philosophy of mathematics the essays discuss the perennial appeal of Platonism in the philosophy of mathematics, the indeterminacy of mathematical ontology, and the legacy of the logicism of Frege and Russell. More general topics discussed include the concept of truth, indeterminacy arguments in ontology, and the status of stipulation in human knowledge.

Contributors include Paul Benacerraf, George Boolos, John Earman and John Norton, Richard Grandy, Jerrold Katz, Penelope Maddy, Adam Morton, Richard Jeffrey, Robert Stalnaker, Mark Steiner and Steven Wagner.